Chumbies are are awesome. RSS feeds are awesome. Why not combine the two? No, the double awesomeness won't hurt anyone, really. The reason is that flash is hard for the unexperienced. Here is a simple way to do it with an already-written program.
I will model it with Instructables, and you should be ready to adjust it according to your needs!
Thanks ewilhelm for the photos!
Step 1: Make Sure You Can Compile Flash!
If you have a Flash developer IDE (I.E. Flash MX), NOT JUST A FLASH PLAYER, then you are all set. If not, look around. If you are a student, the school may have it, someone around work may have it.
If not, I'm sure a group of flash-makers will form in the comments and will be happy to do it for you.
NOTE: My photos were taken on Flash Pro 8, so it may look slightly different than what you are using, but the basic principles are the same.